A standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) and 4 suits (spades, hearts, diamonds, and clubs), such that there is exactly one card for any given rank and suit. The deck is randomly arranged. What is the probability that (a) the top card is an ace or a king. (b) the top card is spades and the second card is clubs. (c) the top card is spades and the second card is an ace.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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A standard deck of 52 cards has 13 ranks (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack,
queen, king) and 4 suits (spades, hearts, diamonds, and clubs), such that
there is exactly one card for any given rank and suit. The deck is randomly
arranged. What is the probability that
(a) the top card is an ace or a king.
(b) the top card is spades and the second card is clubs.
(c) the top card is spades and the second card is an ace.
(d) the top 3 cards are all spades.
(e) the top 4 cards include 3 different ranks, with one rank apprears twice
(for example, an ace of hearts, a 3 of clubs, a 3 of hearts, and a 7 of
spades). 

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